You estimated a regression model using annual returns of ExxonMobil (as a dependent variable) and of the market (as an independent variable). The R-squared of this regression is 0.2, and the total variance of ExxonMobil's returns in the estimation window is 0.0625. In this case, the variance of the unsystematic (or idiosyncratic) component of ExxonMobil's returns is:

use Simpson's 3/8th Rule on the first 3 segments, and multiple application of Simpson's 1/3rd Rule on the rest of the segments.

?(?)=400?⁵−900?⁴+675?³−200?²+25?+0.2

a = 0.12
b = 1.56
n = 7

The number of orders that come into a mail-order sales office each month is normally distributed with a population mean of 298 and a population standard deviation of 15.4. For a particular sample size, the probability is 0.2 that the sample mean exceeds 300. How big must the sample be?

1. What sample size is required to achieve a ME of ±4% at 90% confidence with an estimatedp = 0.3? Show how you arrived at your solution for full credit.

2. If a sample proportion is unknown, what sample size is required to achieve a ME of ±2% at 98% confidence ? Show how you arrived at your solution for full credit.

Shown below are the number of trials and success probability for some Bernoulli trials. Let X denote the total number of successes.

n = 6 and p = 0.3

Determine ​P(x=4​) using the binomial probability formula.

b. Determine ​P(X=4​) using a table of binomial probabilities.

Compare this answer to part​ (a).

The weights of ice cream cartons are normally distributed with a mean weight of 8 ounces and a standard deviation of 0.3 ounce.

​(a) What is the probability that a randomly selected carton has a weight greater than 8.09 ​ounces?

​(b) A sample of 16 cartons is randomly selected. What is the probability that their mean weight is greater than 8.09

ounces?

Weights of 10-ounce bag corn chips follow a normal distribution with µ=10 and σ=0.3 ounces. Find the probability that

–(i) the sample mean weight of 49 randomly selected bags exceeds 10.25 ounces.

–(ii) the sample mean weight of 49 randomly selected bags is less than 10.20 ounces.

Suppose the alphabet is S = {A B C D} and the known probability distribution is P_A = 0.3, P_B = 0.1, P_C = 0.5, and P_D = 0.1. Decode the Huffman coding result {11000010101110100} to the original string based on the probability distribution mentioned above. The codeword for symbol “D” is {111}. Please writing down all the details of calculation.

•Bonnie is 36 weeks and her physician is concerned that the fetus is showing signs of distress.  She orders a “lung profile” which consists of determining the L/S ratio and measuring the percent phosphatidylglycerol (PG) on amniotic fluid.  The results are:

•L/S ratio = 1.0

•PG ratio = 0.3%

1.What is the interpretation of these test results?

Harvey’s REIT is a company that invests in income generating land and buildings. Since Harvey’s is organized as a REIT it must pay out most if not all of its income to shareholders as a dividend. Since the firm is a “pass through” vehicle (passes income straight threw to investors), the REIT pays no taxes (its investors get taxed at the personal level with all income treated as ordinary income). With little retained earnings, new real estate acquisitions are debt or equity financed.

Harvey has two categories of investment. One category is hotels and the second is land for special events parking. The land business is very interesting because you can simply buy the land and there is little or no working capital or capital expenditure needs since the land is often just fields near ballparks, state fairs, concert facilities, etc…

For most of Harvey’s businesses, the cash flow grows at roughly the inflation rate. Hotel fares and parking rates trend up with inflation. Acquisitions rarely add much value, since they are bought in competitive real estate markets. What you pay is pretty close to the discounted cash flow value of what you buy. No acquisitions are currently on the radar and most believe that there should be little “value from future acquisitions” in Harvey’s REIT share prices.

Harvey has entertained breaking up the two units perhaps by divesting one and keeping the other. He wonders what each unit is worth. Here are the cash flows of each business

Hotels: FCF = 90m upcoming year

Parking land FCF = 30m upcoming year

Both business are expected to grow their FCF at 2.4% in perpetuity (due to inflation)

Recall from your prior classes a growing perpetuity is worth:  

Value now = FCF(upcoming year) / (discount rate on FCF – growth rate in perpetuity)

For the most part, given the absence of taxes, it is believed that the firm’s situation approximates perfect market conditions (assuming debt is not 75% plus of total financing which could raise bankruptcy concerns).

Similar (non-taxed) REITS have the following data:

Pure plays (MV stands for market Value and all figures in millions):

The land parking business is unique in the world of publicly traded equities. There are no pure plays out there. All the above firms with D/E below 1.1 are able to borrow at approximately 4.5%. The market risk premium is 5% and the risk free rate is 4.5%. The same is true for Harvey.

Harvey currently has market value of debt = 1000m

Harvey has a market value of equity = 1500m

Harvey has an equity beta of 0.9.

Harvey does not “allocate debt” between divisions. He views the debt ratio of each to be the same.

Assume that Harvey views the market valuation of his firm as likely accurate – he believes that markets are “efficient.” He also views the valuation of competitors as reasonably accurate. He thinks the listed hotel competitors have properties with fairly similar risk, but realizes there may be slight errors in beta estimates (up or down) and averages of beta will have less errors.

How can Harvey figure out the value of his hotel business (not equity or debt pieces, the whole value) and what is the estimate for it? Show the steps for doing so for partial credit

What is the value of the Land business, its’ WACC, and its’ unlevered beta?

Assume that no divestiture takes place. If the Land business got an unexpected opportunity to acquire a piece of land that would generate FCF = 2m growing at 2.4% in perpetuity, and it had an asking price of 48m, should it do the deal? Why or why not?

Some at the firm say that 2/48 = 4.1667%. They note that the accounting return is not even sufficient to cover the cost of borrowing (if the project is financed with all debt) and therefore the project should not be taken. Does this logic make sense? Explain why or why not? (An explanation of what is right or wrong with argument would be useful.